Peril doesn't start to cause fury (5)
I believe the answer is:
anger
'fury' is the definition.
(fury is intense anger)
'peril doesn't start' is the wordplay.
'peril' becomes 'danger' (synonyms).
'doesn't start' means to remove the first letter.
'danger' with its initial letter taken away is 'ANGER'.
'to cause' is the link.
(Other definitions for anger that I've seen before include "Provoke annoyance" , "Heat" , "Strong displeasure" , "One of the seven deadly sins" , "Wrath, fury" .)